Finite Group Databasebeta

← #20249680

Subgroups — #20249680

Order 6016.

804 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093997C212yesmaximal, complemented
2C2×#13093996C212yesmaximal, complemented
3C2×#13093995C212yesmaximal, complemented
4#15689046C212yesmaximal, complemented
5#15689032C211yesmaximal, characteristic, complemented
6#15689031C212yesmaximal, complemented
7#15688997C212yesmaximal, complemented
8#15688995C211yesmaximal, characteristic, complemented
9C47×#392C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12C22×C22⋊D47C2212yes—
13C22×C22⋊D47C2212yes—
14C23×Dic47C2211yescharacteristic
15C22×C4×D47C2212yes—
16#13093997—28no—
17#13093996—28no—
18#13093995—28no—
19C2×C4⋊Dic47C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2211yescharacteristic
29C22×D4×C47C2212yes—
30C22×D4×C47C2211yescharacteristic
31C2×C22⋊C4×C47C2212yes—
32C2×C22⋊C4×C47C2211yescharacteristic
33#95×C47C2211yescharacteristic
34C24×C47C2312yes—
35C24×C47C2311yescharacteristic
36C23×D47C2312yes—
37C2×D4×C47—24no—
38C2×D4×C47—24no—
39C2×D4×C47—42no—
40C2×D4×C47—42no—
41C2×D4×C47—41no—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C2×C22⋊D47—24no—
46C2×C22⋊D47—24no—
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—24no—
50C2×C22⋊D47—24no—
51C2×C22⋊D47—42no—
52C2×C22⋊D47—42no—
53C2×C22⋊D47—42no—
54C22×Dic47—24no—
55C22×Dic47—41no—
56C22×Dic47C2312yes—
57C22×Dic47C2312yes—
58C22×Dic47C2312yes—
59C2×D188—24no—
60C2×D188—41no—
61C2×C4×D47—24no—
62C2×C4×D47—24no—
63C2×C4×D47—42no—
64C22⋊C4×C47—24no—
65C22⋊C4×C47—41no—
66C22⋊Dic47—24no—
67C22⋊Dic47—24no—
68C22⋊Dic47D414yescomplemented
69(C2×D47)⋊C4—42no—
70(C2×D47)⋊C4D418yescomplemented
71C4⋊Dic47—24no—
72Dic47⋊C4—24no—
73Dic47⋊C4—24no—
74C23×C47—22no—
75C23×C47—21no—
76C23×C47—22no—
77C23×C47—21no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47C2×D412yes—
86C23×C47C2411yescharacteristic
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—22no—
91C22×D47—22no—
92C22×D47—22no—
93C22×D47C2×D414yes—
94D4×C47—48no—
95D4×C47—44no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47C2×D414yes—
103C22⋊D47—48no—
104C22⋊D47—48no—
105C22⋊D47—48no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—44no—
114C2×Dic47C2×D414yes—
115C2×Dic47C2×D414yes—
116D188—44no—
117C4×D47—48no—
118C22×C47—22no—
119C22×C47—24no—
120C22×C47—42no—
121C22×C47—41no—
122C22×C47—41no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47C22×D412yes—
131C22×C47C22×D411yescharacteristic
132C22×C47H(5,𝔽2)12yes—
133C22×C47H(5,𝔽2)11yescharacteristic
134C22×C472−1+411yescharacteristic
135C2×D47—24no—
136C2×D47—24no—
137C2×D47—24no—
138C2×D47—42no—
139C2×D47—42no—
140C2×D47—42no—
141C2×D47—42no—
142C4×C47—24no—
143C4×C47—41no—
144C4×C47—41no—
145Dic47—24no—
146Dic47—24no—
147Dic47—42no—
148#2675—471nomaximal, Sylow
149C2×C47—42no—
150C2×C47—82no—
151C2×C47#53711yescharacteristic
152C2×C47#53712yes—
153C2×C47D4212yes—
154C2×C47D4211yescharacteristic
155C2×C47#56011yescharacteristic
156D47—44no—
157C2×#121—472no—
158C2×#121—472no—
159C2×#121—472no—
160#396—472no—
161#392—472no—
162#392—471no—
163#392D4711yescharacteristic, complemented
164#385—471no—
165#385—472no—
166C47#267511yescharacteristic, complemented, Sylow
167C22×D4—472no—
168C22×D4—472no—
169C22×D4—472no—
170C22×D4—471no—
171C22×D4C2×D4712yes—
172C22×D4C2×D4711yescharacteristic
173C23×C4—471no—
174C23×C4—472no—
175#121—948no—
176#121—948no—
177#121—948no—
178C2×C4⋊C4—472no—
179C2×C4⋊C4—472no—
180C2×C4⋊C4—472no—
181C2×C22⋊C4—471no—
182C2×C22⋊C4—472no—
183C2×C22⋊C4—472no—
184C2×C22⋊C4—472no—
185C2×C22⋊C4—472no—
186C2×C22⋊C4C2×D4712yes—
187C2×C22⋊C4C2×D4711yescharacteristic
188#95—472no—
189#95—471no—
190#95C2×D4711yescharacteristic
191C24—472no—
192C24C22×D4712yes—
193C24C22×D4711yescharacteristic
194C2×D4—24no—
195C2×D4—24no—
196C2×D4—42no—
197C2×D4—41no—
198C2×D4—42no—
199C2×D4—944no—
200C2×D4—944no—
201C2×D4—944no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—944no—
205C2×D4—944no—
206C2×D4—1881no—
207C2×D4—1882no—
208C2×D4—1882no—
209C2×D4—1882no—
210C22×C4—472no—
211C22×C4—472no—
212C22×C4—472no—
213C22×C4—944no—
214C22×C4—944no—
215C22×C4—944no—
216C22×C4—1882no—
217C22×C4—1881no—
218C22×C4C22×D4711yescharacteristic
219C22×C4C22×D4711yescharacteristic
220C22×C4C22×D4712yes—
221C4⋊C4—944no—
222C4⋊C4—944no—
223C4⋊C4—944no—
224C22⋊C4—24no—
225C22⋊C4—41no—
226C22⋊C4—474no—
227C22⋊C4—478no—
228C22⋊C4—944no—
229C22⋊C4—944no—
230C22⋊C4—1882no—
231C23—22no—
232C23—21no—
233C23—22no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—474no—
243C23—942no—
244C23—942no—
245C23—942no—
246C23—942no—
247C23—942no—
248C23—942no—
249C23D4×D4712yes—
250C23C23×D4711yescharacteristic
251D4—48no—
252D4—44no—
253D4—1884no—
254D4—1888no—
255D4—1888no—
256D4—1888no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—474no—
264C2×C4—474no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—1888no—
273C2×C4—1884no—
274C2×C4D4×D4714yes—
275C22—24no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—944no—
288C22—944no—
289C22—944no—
290C22—1882no—
291C22—1882no—
292C22—1882no—
293C22—1882no—
294C22C2×D4×D4711yescharacteristic
295C22C2×D4×D4712yes—
296C22#1309406912yes—
297C22#1309406911yescharacteristic
298C22#1309407111yescharacteristic
299C4—24no—
300C4—41no—
301C4—41no—
302C4—944no—
303C4—944no—
304C4—1882no—
305C2—42no—
306C2—82no—
307C2—1884no—
308C2#1568970011yescharacteristic
309C2#1568970212yes—
310C2#1568975512yes—
311C2#1568975811yescharacteristic
312C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2675
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#13093997C2semidirect
2. C2×#13093996C2semidirect
3. C2×#13093995C2semidirect
4. #15689046C2semidirect
5. #15689032C2semidirect
6. #15689031C2semidirect
7. #15688997C2semidirect
8. #15688995C2semidirect
9. C47×#392C2semidirect
68. C22⋊Dic47D4semidirect
70. (C2×D47)⋊C4D4semidirect
163. #392D47semidirect
166. C47#2675semidirect